Search for the Σ(1380)1/2⁻ state in $Λ^+_c → γ π^+ Λ$ decay by triangle singularity

In this work, we investigate the resonance production in Λ⁺c → γ π⁺ Λ decay through the triangle singularity (TS) mechanism, within an effective Lagrangian approach. We find that the appropriate loop decay process could develop a triangle singularity in the invariant mass MπΛ around $1.35$ GeV, with the shape depending on the quantum numbers of Σ^* states that couple to the final πΛ system. Especially, the Σ(1380)1/2⁻ state newly predicted in the pentaquark model, if exists, significantly enhances the TS contribution and sharpens the TS peak due to the S-wave Σ^*πΣ vertex in the loop. Therefore, the existence of the Σ(1380)1/2⁻ state can be examined by measuring the TS signal in Λ⁺c → γ π⁺ Λ. Considering also possible tree-level diagrams, we additionally obtain the branching ratio Br(Λ⁺c → γ π⁺ Λ) 1.5× 10⁻⁵. We suggest the investigation of this reaction by future BESIII, LHCb, and Belle experiments.